This is a duplicate of this query
(I was asked to shift the query from economics.stackexchange to Cross Validated SE.)
Lets say I am building a market model to estimate the beta of a stock with respect to a index of stocks.
The beta maybe Constant / Autoregressive of order 1 / doing a random walk. I realize there are time varying regression approaches for estimation of the above parameters IF I have an idea of the true nature of the parameters.
What is not clear to me if there are economic principles available to think about the nature of the parameters.
Should I assume that the intercept and slope have the same nature ( ie. they are both constant / Autoregressive of order 1 / doing a random walk.)
Is it possible that the intercept and slope have different characteristics ? Eg. the intercept is doing a random walk while the slope is AR1.
Can someone share the intuition behind this ? What should I be reading to understand this ?